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arXiv · 2610.39015

Synge's Theorem and a Sphere Theorem in Weighted Intermediate Ricci Curvature

Hasan M. El-Hasan·Curtis Pro
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Abstract

Using the tools developed by Kennard, Wylie, and Yeroshkin for weighted sectional curvature bounds, we generalize a theorem of Wilhelm to show that Synge's Theorem holds for manifolds with density that have positive weighted intermediate Ricci curvature and a sufficiently large first systole. Furthermore, we provide a sphere theorem for compact manifolds with positive weighted intermediate Ricci curvature.

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Hasan M. El-Hasan, Curtis Pro. 2026-10-28. Synge's Theorem and a Sphere Theorem in Weighted Intermediate Ricci Curvature. https://arxiv.org/abs/2610.39015

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